Ratcheting screwdrivers are known as are reversible bit screwdrivers, the latter having a reversible bit for a 2-in-1 screwdriver or two reversible bits in a reversible shank for a 4-in-1 screwdriver. The present invention is intended to provide a combination of the convenience of a multiple-bit screwdriver, especially a 4-in-1, with the usefulness of a ratcheting screwdriver in a construction strong enough for industrial or professional use.